I would like to try out the Petrov-Galerkin Enrichment Method (Barrenechea et al 2007) for a mixed-poisson/Darcy equation.Here is the link to the paper: http://www.sciencedirect.com/science/article/pii/S0045782507000059 Basically, this method starts with the P1/P0 combination and enriches both velocity and pressure trial functions with multi-scale functions. Is this easily doable within Firedrake? Thanks, Justin
-----BEGIN PGP SIGNED MESSAGE----- Hash: SHA1 On 15/07/15 11:46, Justin Chang wrote:
I would like to try out the Petrov-Galerkin Enrichment Method (Barrenechea et al 2007) for a mixed-poisson/Darcy equation.Here is the link to the paper:
http://www.sciencedirect.com/science/article/pii/S0045782507000059
Basically, this method starts with the P1/P0 combination and enriches both velocity and pressure trial functions with multi-scale functions. Is this easily doable within Firedrake?
Can you say a little more? It looks like I enrich the velocity space with RT0 but somehow only locally (such that I can solve a local H(div) problem to get a correction?), but I don't really know enough about the method to say whether you could do it. Lawrence -----BEGIN PGP SIGNATURE----- Version: GnuPG v1 iQEcBAEBAgAGBQJVpjvEAAoJECOc1kQ8PEYvX7AIAIBsjOhcP3kDIa5gaNB+Fc96 TpAQ2Rx+E5jKrb8CSUcC1g8CZ9I+87uu/0A9Sr5jsqChhY7rvpxYp7nFISJdLibe vrh/AS+XD/ztkBgDPd+sYN9gUMV6RoyouMWNSUSLRlctPAsfRB9MqTuTjmf7YxvP Gjsdffm97BxQwHYwLPWm3qoiZ2t656D5qWgsR/co5PVHMZanGSj5dn7k4bzVYUCZ ox27IT0LUErXm6P5kmm7exXK3l0TWVmF2N+ABcmBBtBpAFft4lIEaE81SxnXPjKg TKlKSW4TCaUO3uSvgukuxM0PrLfuZbNvJCxfY5au1r1q5JWQHXdeDCgRiyCUiZ0= =d/jn -----END PGP SIGNATURE-----
Lawrence, It looks to me that the trial functions are enriched on the edge residuals. I am guessing that's what was meant by the multiscale aka "enrichment" functions. This other paper written by the same guys offers some explanation: http://epubs.siam.org/doi/pdf/10.1137/080724381 My only question is what the Finite Element Spaces would look like within Firedrake - would it be a concatenation of two separate function spaces (P1 and RT0) or would the basis function look completely different? I could be wrong, I may need to do a little more research on this first. Thanks, Justin On Wed, Jul 15, 2015 at 5:54 AM, Lawrence Mitchell < lawrence.mitchell@imperial.ac.uk> wrote:
-----BEGIN PGP SIGNED MESSAGE----- Hash: SHA1
On 15/07/15 11:46, Justin Chang wrote:
I would like to try out the Petrov-Galerkin Enrichment Method (Barrenechea et al 2007) for a mixed-poisson/Darcy equation.Here is the link to the paper:
http://www.sciencedirect.com/science/article/pii/S0045782507000059
Basically, this method starts with the P1/P0 combination and enriches both velocity and pressure trial functions with multi-scale functions. Is this easily doable within Firedrake?
Can you say a little more? It looks like I enrich the velocity space with RT0 but somehow only locally (such that I can solve a local H(div) problem to get a correction?), but I don't really know enough about the method to say whether you could do it.
Lawrence
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-----BEGIN PGP SIGNED MESSAGE----- Hash: SHA1 On 15/07/15 21:03, Justin Chang wrote:
Lawrence,
It looks to me that the trial functions are enriched on the edge residuals. I am guessing that's what was meant by the multiscale aka "enrichment" functions. This other paper written by the same guys offers some explanation:
http://epubs.siam.org/doi/pdf/10.1137/080724381
My only question is what the Finite Element Spaces would look like within Firedrake - would it be a concatenation of two separate function spaces (P1 and RT0) or would the basis function look completely different? I could be wrong, I may need to do a little more research on this first.
So if it is just the concatenation, I thought this might be straightforward, but it turns out not. In particular, the basis functions for P1 and RT0 don't transform the same way. Lawrence -----BEGIN PGP SIGNATURE----- Version: GnuPG v1 iQEcBAEBAgAGBQJVp7CQAAoJECOc1kQ8PEYvZqwIAJMlkvKPA1KtZud3mE1wYwiy wKawuDoaZVrMCcVjygy5H8/nPQloEBRHP3qLGPlsDdofoNpK/Imgr4uRNmr06uNH F7pJ0H6g+5CKjcklBxDTyCX3vxzPa8nA4KjWXAsoKtV6QJL+xFrcAUBQqDKqilFm xY5Se50lg/DOO4NNUh9tPOLGPBuAq52SMrP7Db78J5IW991CS/QyRQJoLm+NIAqY sVoL7a5uhPAsC+I/RUMJ8VxvEarWg9ZrDeyirSBht7CUa/P9rZ/Fc5HCHOrdk4OO 799F2+t5AxVOKCX7FOWsnR00BLQa4potKYKvcOT6VLjFwqmO9jd7y/ACkspxps0= =8rZN -----END PGP SIGNATURE-----
participants (2)
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Justin Chang
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Lawrence Mitchell